Describe the translation of f(x) = |x|.

Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction. Samuel traveled 3km/h fa

12345 [234]

Samuel was going with 40 km/h and Heather was going with 37 km/h

Step-by-step explanation:

Starting at the same point at the same time, Samuel and Heather rode their bikes in the same direction

Samuel traveled 3 km/h faster than Heather
After 3.5 h Samuel stopped for a half-hour break, but Heather kept going
Heather was 8 km ahead of Samuel

We need to find how fast each was going

Assume that Heather's speed is x km/h

∵ Heather's speed = x km/h

∵ Samuel traveled 3 km/h faster than Heather

∴ Samuel's speed = x + 3 km/h

The formula of the distance is distance = speed × time

∵ Samuel travel for 3.5 hours

- Find the distance that Samuel traveled in 3.5 h

∴ Samuel distance = (x + 3) × 3.5

- Multiply the bracket by 3.5 to simplify

∴ Samuel distance = 3.5x + 10.5

∵ Samuel took a break for half hour

∵ Heather kept going

∵ At the end of the break, Heather was 8 km ahead of Samuel

- That means Heather was going for 4 hours (3.5 + 0.5), and her

distance is longer than Samuel distance by 8 km

∴ Heather distance = x × 4 = 4x

- Subtract the distance of Samuel from the distance of Heather

and equate the difference by 8

∵ 4x - (3x + 10.5) = 8

∴ 4x - 3x - 10.5 = 8

- Add the like terms in the left hand side

∴ 0.5x - 10.5 = 8

- Add 10.5 to both sides

∴ 0.5x = 18.5

- Divide both sides by 0.5

∴ x = 37

∵ x represents Heather's speed

∴ Heather's speed = 37 km/h

∵ x + 3 represents Samuel's speed

∴ Samuel's speed = 37 + 3 = 40 km/h

Samuel was going with 40 km/h and Heather was going with 37 km/h

Learn more:

You can learn more about the equation of motion in brainly.com/question/568302

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3 0

3 years ago

HELPPP ME PLEASE I REALLY NEED HELP

aliya0001 [1]

<h3>Answer: choice F) 12 & 1/2 square yards.</h3>

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We'll use this formula

a & b/c = (a*c + b)/c

to convert from a mixed number to an improper fraction.

Let's convert the first mixed number to an improper fraction

a & b/c = (a*c + b)/c

3 & 3/4 = (3*4 + 3)/4

3 & 3/4 = 15/4

Repeat the same idea for the second mixed number as well

a & b/c = (a*c + b)/c

3 & 1/3 = (3*3 + 1)/3

3 & 1/3 = 10/3

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In short we have

3 & 3/4 = 15/4
3 & 1/3 = 10/3

Doing these conversions is useful to be able to multiply the values like so:

(15/4)*(10/3) = (15*10)/(4*3) = 150/12 = (6*25)/(6*2) = 25/2

Now use your calculator to find that 25/2 = 12.5

We can then say....

12.5 = 12 + 0.5 = 12 + (1/2) = 12 & 1/2

The answer is choice F) 12 & 1/2 square yards.

6 0

2 years ago

Drag the numbers to order them from least to greatest. 2/3 -4 1/2 1/4 -1/2 2 1/3

kotegsom [21]

The larger the negative number the smaller the value:

The order would be:

-4, -1/2, 1/4, 1/3, 1/2, 2/3, 2

5 0

2 years ago

Read 2 more answers

If ( 43.65 ) ( 8.79 ) / x = ( 0.4365 ) ( 87.9 ) then value of x is:

strojnjashka [21]

Answer:

(d) 10

Step-by-step explanation:

Multiply by x and divide by its coefficient:

(43.65)(8.79) = (0.4365)(87.9)x

(43.65)(8.79)/((0.4365)(87.9)) = x

At this point, any calculator can give you the answer. It is, perhaps, more satisfying to work out the answer without a calculator.

x = (43.65)/(0.4365) × (8.79)/(87.9)

In the first quotient, the numerator is 100 times the denominator; in the second, the denominator is 10 times the numerator.

x = (100) × (1/10) = 100/10

x = 10

_____

Moving the decimal point to the right 1 place multiplies the numerical value by 10.

5 0

3 years ago

The slopes of perpendicular lines are? will give brainliest for correct answer

Murrr4er [49]

Answer:

opposites

Step-by-step explanation:

5 0

2 years ago